Things other than the temperature that could affect whether or not the coat is necessary: Is it raining? a wet dog will get cold quicker. How long/thick is the fur? thin coats of fur will be less efficient at keeping the dog warm than thick. Is it windy? Wind blows warm air out of the fur. How big is the dog? Size & body fat will affect the rate of heat loss. How active is the dog? A dog doing lots of fetching will keep warmer than a dog ambling along the pavement
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GriffinEvoDec 27 '12 at 11:54

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Clues as to whether the coats are necessary: Is the dog shivering? if yes, give it a coat. Is the dog panting? yes, take the coat off before you bake the thing!
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GriffinEvoDec 27 '12 at 11:56

@rg255 would you like to post your comments as an answer?
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cryptic ツJan 26 '13 at 3:24

1 Answer
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Things other than the temperature that could affect whether or not the coat is necessary: Is it raining? a wet dog will get cold quicker. How long/thick is the fur? thin coats of fur will be less efficient at keeping the dog warm than thick. Is it windy? Wind blows warm air out of the fur. How big is the dog? Size & body fat will affect the rate of heat loss. How active is the dog? A dog doing lots of fetching will keep warmer than a dog ambling along the pavement.

Clues as to whether the coats are necessary: Is the dog shivering? if yes, give it a coat. Is the dog panting? yes, take the coat off before you bake the thing!

this probably does not fully answer the question "If the temperature outside is 45°F who would feel colder?" but as requested by the OP I have posted my comments as an answer. I would expect a dog without a "doggy sweater" to be better able to cope with the cold than a human not wearing a "people sweater" or any clothes, just like the dog, if you want to make it a fair test!